Question

Suppose a business has pricing and cost information as follows::

Price and Cost Information Amount
Selling Price per Unit $10.00
Variable Cost per Unit $5.00
Total Fixed Cost $100

For the upcoming period, the company wishes to generate operating income of $400. Given the cost and pricing structure for the company’s product, how many units must the company sell to attain its target income?

Create a contribution margin income statement to check your previous work. Enter all amounts as positive numbers.
Sales $
Total variable expense
Total contribution margin $
Total fixed expense
Operating income $

Answer 1

To achieve a target operating income of $400, the company must sell 100 units. This is determined by calculating the contribution margin per unit and then dividing total fixed costs plus desired operating income by this margin.

Step-by-step explanation:

To determine how many units the company must sell to achieve its target operating income of $400, we calculate the break-even point and the additional units needed for the desired profit.

Firstly, calculate the contribution margin per unit, which is the selling price per unit minus the variable cost per unit:

• Selling Price per Unit = $10.00
• Variable Cost per Unit = $5.00
• Contribution Margin per Unit = $10.00 - $5.00 = $5.00

Next, divide the total fixed cost plus the desired operating income by the contribution margin per unit to find the number of units needed:

• Total Fixed Cost = $100
• Desired Operating Income = $400
• Units Required = ($100 + $400) / $5.00 = 100 units

The contribution margin income statement would reflect the following with 100 units sold:

• Sales (100 units × $10.00) = $1,000
• Total Variable Expense (100 units × $5.00) = $500
• Total Contribution Margin ($1,000 - $500) = $500
• Total Fixed Expense = $100
• Operating Income ($500 - $100) = $400

By selling 100 units, the company meets its target operating income of $400.